What are the realistic possibilities of a married Byzantine Catholic man becoming a priest in the United States?

The few people I know in this process are seemingly stuck in various stages of the decernment process.

What are some common hurdles that others may have experienced (example: young kids, young marriage, debt)?

Are certain Byzantine churches more open to this than others?

I don’t know the answer to all of your questions, but I do know several married, American priests who were ordained in the United States: two Melkites, two Ruthenian, one Ukrainian, one Romanian. Two of them are retired, with grown children. The rest are young and raising families. All of them have a source of income outside of that which is provided by their parishes.

What are the realistic possibilities of a married Byzantine Catholic man becoming a priest in the United States?

Marriage is no longer an impediment to ordination in the US. There have been a number of ordinations of married men here in the past decade. There are also men who are married or likely to be married among the seminarians at SS Cyril and Methodius. In addition the BCC now has a substantial number of married priests who have immigrated from Slovakia and Ukraine